Question

A church is bringing a group of its members to a "clean comedians" show. If they bring 15 people, it will cost $10 each. For each additional person the church brings, the price per ticket will go down $0.20. Groups are limited to 35 people because of the seating capacity of the auditorium.
What will it cost the church to bring 18 members? (Round your answer to the nearest cent.)

It costs the church $______ to bring 18 members to the "clean comedian" show.

Use your model to find the total cost of bringing a group of 26 people. (Round your answer to the nearest cent.)

It costs $_____to bring 26 members to the show.

If the church can only afford to pay $210.80 for this trip, how many people can the church bring? (Enter your answers from smallest to largest.)

The church can bring either______(smaller value) or______(larger value) people to the show for $210.80

Answer 1

Answer:

a) $169.2

b) $202.8

c) the church can bring either 31 or 34 members

Step-by-step explanation:

For each person the church brings that exceeds 15, the ticket price goes down by $0.20

18 members exceed 15 by 3.

This means that for 3 persons the church brings that exceeds 15, we have 3*0.20 = $0.60

The price of the ticket will now be

10 - 0.6 = $9.40

For the 18 members, we now have

18*9.4 = $169.2

b) The model for bringing a number of people at a particular cost = C(x)

x is the number of people that exceeds 15

C(x) = (15+x)(10-0.2x)

C(x) = 150 - 3x + 10x - 0.2x^2

= 150 + 7x - 0.2x^2

In bringing 26 people to the show, it is 11 more than 15

C(11) = 150 + 7(11) - 0.2(11)^2

C(11) = 150 +77 - 24.2

= $202.8

c) if the church can only afford $210.8, to solve x, we have

150 + 7x - 0.2x^2 = 210.8

-0.2x^2 + 7x + 150 = 210.8

-0.2x^2 + 7x + 150 - 210.8 = 0

-0.2x^2 + 7x -60.8 = 0

(-b +/-√b^2 - 4ac) / 2a

a = -0.2 , b = 7 c = -60.8

(-7 +/-√7^2 - 4(-0.2)(-60.8)) / 2(-0.2) = 0

(-7 +/-√49 - 48.64) / -0.4 = 0

(-7 +/-√0.36) / -0.4 = 0

(-7 +/- 0.6) / -0.4 = 0

(-7+0.6)/-0.4 or (-7 - 0.6)/-0.4

(-6.4)/-0.4 or (-7.6)/- 0.4

16 or 19

So we have (15+16) = 31 members

(15+19) = 34 members

The church can bring either 31 members or 34 members